Subcellular resolution 3D light field imaging with genetically encoded voltage indicators

Light field microscopy (LFM) enables high signal-to-noise ratio (SNR), light efficient volume imaging at fast frame rates, and has been successfully applied to single-cell resolution functional neuronal calcium imaging. Voltage imaging with genetically encoded voltage indicators (GEVIs) stands to particularly benefit from light field microscopy’s volumetric imaging capability due to high required sampling rates, and limited probe brightness and functional sensitivity. Previous LFM studies have imaged GEVIs to track population-level interactions only in invertebrate preparations and without single cell resolution. Here we demonstrate sub-cellular resolution GEVI light field imaging in acute mouse brain slices resolving dendritic voltage signals localized in three dimensions. We characterize the effects of different light field reconstruction techniques on the SNR and signal localization and compare the SNR to fluorescence transients imaged in wide field. Our results demonstrate the potential of light field voltage imaging for studying dendritic integration and action potential propagation and backpropagation in 3 spatial dimensions.

1 Introduction or two-photon microscopy approaches as they are point scanning. Sequential sampling of each 23 pixel greatly reduces imaging bandwidth, and the fast frame rates required for voltage imaging 24 necessitates short dwell times and therefore few collected photons. This restricts Poisson-noise 25 limited SNR to low levels, making point scanning voltage imaging applicable to a limited number 26 of experimental paradigms. 12, 18-20 27 Fluorescence excitation parallelization into multiple spots, 21-27 blobs, 28, 29 lines, 30-32 sheets, 33-40 28 or specified patterns 41-45 increases the photon budget, enabling functional volumetric imaging or 29 single-plane imaging at increased speeds. A small number of these have been applied to imaging 30 voltage in 2 dimensions, 26, 31, 42, 45 however they are not able to image neuronal processes in 3D. 31 Many of these techniques also trade-off reduced robustness to scattering compared to single-point 32 scanning modalities for the increased excitation from parallelization. images are typically parameterized by the 4D function L(u, v, x, y), where each lenslet subimage 48 is L(u, v, ·, ·) and the same specific pixel under each subimage is L(·, ·, x, y). The 'native LFM 49 resolution' with which the object is laterally sampled is given by the microlens pitch divided by 50 the objective magnification, much worse than the corresponding wide field resolution. In exchange 51 the microlenses provide angular information that can be used to render views of the object from 52 different perspectives, focus on different planes, and reconstruct 3D volumes all from a single 2D 53 frame. This technique converts a key disadvantage of wide field 1P fluorescence excitation, lack 54 of optical sectioning, into an advantage, as out-of-focus light renders 3D information about the 55 sample. 56 Two prominent algorithms for reconstructing source volumes from LFM images have been de-57 scribed, synthetic refocusing 49 and 3D deconvolution. 50 Synthetic refocusing relies on a ray optics 58 model of LFM image formation to reconstruct images at the native LFM resolution equivalent to 59 those of a wide field microscope focused at any axial plane in the sample. Focal stacks can be 60 generated similar to standard microscope z-stacks by combining images reconstructed at multiple 61 axial depths. Each pixel in the refocused image is a weighted sum of light field image pixels, 62 meaning refocusing is fast. The reconstructed images, however, suffer from the same blur due to 63 lack of optical sectioning as a standard wide field microscope. 64 An alternative approach is based on reconstruction of the source volume using a forward tion. 54-57 The source volume is also reconstructed with less axial blur than in the refocused case, 74 increasing axial signal discriminability. 75 Electrical length constants in neurons are on the scale of tens to hundreds of microns, making 76 increased lateral pixel size less disadvantageous for voltage imaging. Over-resolving electrical 77 fluctuations by imaging at or below the diffraction limit is typically unnecessary and can even hurt 78 SNR by increasing the relative impact of non-Poisson noise such as read noise. Spatial resolu-79 tion is therefore often sacrificed in voltage imaging experiments to increase speed or SNR. Many 80 such experiments use low read noise, high sensitivity CCD sensors featuring low pixel counts, 81 with pixels often measuring several microns across in the sample plane. Even with higher pixel 82 count detectors, the relatively low sensitivity of many voltage probes means multiple pixels are 83 often binned to increase SNR to acceptable levels. LFM's decreased native lateral sampling rate 84 therefore suits voltage imaging well, and deconvolution of LFM voltage imaging time series can 85 be implemented without oversampling to reduce computational cost. 86 LFM has successfully imaged calcium over large volumes in C. elegans and zebrafish, 58, 59 and 87 in both head-fixed and behaving mice. 60-62 Voltage dynamics have also been imaged successfully 88 without single-cell resolution in Drosophila 63 and larval zebrafish 64 as part of whole brain imaging 89 setups alongside calcium imaging. LFM has not, to our knowledge, been applied to studying sub-90 cellular or single-cell resolution voltage dynamics in any sample, despite its apparent suitability. In 91 this study we apply LFM to sub-cellular GEVI imaging in acute mouse brain slices. We combine 92 this technique with a recently reported transgenic strategy driving sparse expression in a random 93 subset of layer 2/3 cortical pyramidal neurons which enables the resolution of single-cell level 94 voltage signals in neuronal somata and dendrites. 65, 66 95 We demonstrate that LFM is able to simultaneously image axially separated dendrites, enabling 96 single-shot capture and localisation of GEVI fluorescence transients in the 3D dendritic arbour. 97 We compare and evaluate deconvolution and synthetic refocusing for different GEVI imaging ap-98 plications, whilst using a coarse deconvolution approach with no lateral oversampling to reduce 99 computational cost. We also apply a recently developed LFM PSF calculation 67 for high NA ob-100 jectives. We show that LFM enables 3D localization of dendritic and somatic GEVI fluorescence This section reproduces methods described in Quicke (2019). 68 We designed our LFM following 106 the principles set out by Levoy et al. (2006). 49 We adapted a wide field imaging system by placing To efficiently use the camera sensor, the exit pupil of the objective should map through the 120 MLA to produce circles on the light field plane that are just touching, requiring that the objective 121 image-side f-number (f/12.5) equal the MLA f-number. We chose an f/10 MLA (MLA-S125-f10, 122 RPC Photonics), an off-the-shelf part which came close to matching whilst being a larger aperture. We reconstructed source volumes using two techniques to compare their performance for single-162 cell voltage data. We calculated (x,y,z,t) volume time series using synthetic refocussing, 49 and 163 ISRA 53, 58 using a PSF calculated using the method described in the section below. RL decon-164 volution 50-52 was also tested on the data, however little discernible difference in the results was 165 observed. We calculated LFM PSFs differently to previously described, 50 using the method described in 168 Quicke et al.  Having obtained our downsampled PSF we deconvolved our volume using a similar procedure to 184 previous studies. A key difference is that only a single 2D convolution was required for each depth 185 in the reconstructed volume for the forwards and backwards projections, respectively, as we did 186 not increase the lateral sampling rate. We applied the deconvolution scheme independently to each 187 frame of the image time sequences, using a cluster to parallelize the data processing. Deconvolu-188 tion of a single frame took around 30 -40 minutes for a 21 iteration deconvolution of 21 z-planes 189 on a single CPU. We employed a large cluster to process the individual frames simultaneously, 190 enabling 5000 frames to be processed overnight. We did not use a parallel algorithm within each 191 deconvolution to leverage, e.g., GPU processing, as the computing resources available to us were 192 better suited to data parallelism. As with previous studies this would greatly increase the rate of 193 individual frames, although it would also likely reduce the number of simultaneous frames that 194 could be deconvolved for typical cluster setups. 195 Synthetic refocusing, based on a ray optics model of light field image formation, is a simpler 196 approach to volume reconstruction that is also much less computationally intensive. Images fo-  We compared the SNR between trials of the same cell for image sequences taken with wide field 220 and light field imaging systems. We compared the SNR between refocused and wide field images 221 for the same number of repeats using ROIs calculated to be the same for both imaging modalities. 222 For 8/12 cells, an extra aperture was introduced into our light field microscope to compensate 223 for chromatic aberration, reducing the light throughput of the microscope by between 1/2 and 3/4 224 during light field imaging compared to the equivalent wide field trials. To account for this, the SNR 225 for these trials was adjusted by a factor equal to the square root of the ratio of the mean brightness 226 of the first imaging trials from the light field and wide field trials. The microscope was realigned 227 to account for chromatic aberration before the final 4/12 cells, meaning the design light throughput 228 of the microscope was the same between light field and wide field trials. For these trials the raw 229 SNR was included in the analysis. We compared the lateral and axial signal spread using a method similar to our previous work. 65 We 232 quantified the neuronal voltage signal strength in each pixel to create 2-or 3-D 'activation maps' 233 by calculating the temporal correlation coefficient of each pixel's time course with a seed time 234 course from the somatic ROI. 235 We compared the spatial autocorrelations of these activation maps to quantify the average sig-236 nal crosstalk between cellular voltage signals. 65 In our previous work we described how the auto-  245 We demonstrated LFM's ability to resolve axially separated structures by imaging a cell with a 246 complex 3D dendritic arbour using both wide field and light field microscopy ( Fig. 1b) and LFM 247 (Fig. 1c). No single plane wide field image was able to simultaneously bring all the dendrites into 248 a good focus (Fig. 1d), however in different planes from a volume reconstructed by deconvolution 249 different dendritic structures could be clearly distinguished (Fig. 1e1 & Fig. 1e2). The same 250 cellular features can clearly be seen in a standard deviation projection through the reconstructed 251 LFM stack (Fig. 1e3) and a wide field z stack through the same cell (Fig. 1b, , 1.3)). We also processed the light field time series using RL deconvolution and 271 found no substantial differences compared to ISRA.  )) localised at different depths. The somatic signal (a1) is maximal in the wide field and native light field focal planes, whilst the apical dendrite (a2) descends into the slice with its ROI localised 15 um deeper. The signal from a basal dendrite (a3) is superficial to the soma, and its best focal depth is difficult to localize due to the broad axial extent of the refocused signal. The basal and apical dendritic fluorescence transients in the wide field time courses have smaller signals than the light field signals as they are out of plane when focused on the soma. c) The normalised signal size for each ROI across different deconvolved (c1) and refocused (c2) depths. Deconvolution increases the axial localisation of signals. The data are an average of 8 sweeps.  (Fig. 3(1) has the largest signal when the LF image is refocused 15 µm deeper into the slice, and 289 the signal in the equivalent wide field ROI is much smaller. The depth-time plots for this ROI from 290 both deconvolved and refocused stacks also clearly show the center of mass of the signal located 291 deeper than the native focal plane (Fig. 3(1), bottom). Signals from a basal dendrite (Fig. 3(3) 292 are similarly larger in the LF image refocused 10 µm shallower than the native focal plane. The 293 corresponding depth-time plots show a slight shift in the signal center of mass to a shallower depth, 294 especially in the refocused case. 295 Plots of signal size as a function of depth for the refocused and deconvolved cases (Fig. 3c 1 &   296 2) show the axial localization as distinctly different planes for each ROI and also demonstrate a key 297 advantage of deconvolved over refocused reconstructions: increased accuracy in axial localization 298 of functional signals.

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The transients from refocused volumes exhibit a larger axial PSF width compared to the decon-301 volved traces (Fig. 3c). Hence these signals are smeared out, reducing distinguishability of signal 302 contributions from different planes. To quantify this effect we generated volumes showing the 303 distribution of functional signal. We generated a time course from an in focus somatic ROI and 304 calculated the temporal correlation coefficient of every pixel in the volume for refocused and de-305 convolved volume time series. Pixels with high correlation coefficients are interpreted as having a 306 large response to the intracellular current injection, and so a volume map of these reveals morphol-307 ogy of structures through which the functional signal propagates. Activation maps from wide field 308 imaging trials show blurring around the soma from out of focus basal dendrites (Fig. 4a). Com-309 paratively, z-projections from a 70 µm region around the soma generated from the deconvolved 310 activation volume (Fig. 4b) reveals the structures that cause this blur. A projection through 70 µm 311 around the focus from the refocused case shows significantly more blurring due to the poor axial 312 sectioning of this technique (Fig. 4c). We used the 3D autocorrelation of these activation maps to 313 quantify the spread of the signal in 3D (see section 2.3.4). We quantified how the peak autocorre-314 lation from each cell, and therefore functional signal contribution, decayed axially. Axial smearing 315 can be seen in reconstructions from both deconvolution and refocusing (Fig. 4d), although the ef-316 fect is much more severe in refocused traces. The smearing appears in the axial autocorrelation as 317 both broadening of the central peak and increased side lobes (Fig. 4e). The central peak width and 318 side lobes decrease with increased deconvolution iteration number ( Fig. 4f & g), thus increasing 319 the axial sectioning. 320 The autocorrelation widths decreased significantly from 1 to 21 iterations (median dropped 321 from 42.5 (37.5, 47.5) µm to 22.5 (12.5, 23.75) µm, z = 0, p = 0.002), and for both cases the 322 axial spread was significantly lower than refocused (median of 47.5 (47.5, 52.5) µm, p = 0.001, 323 p = 0.002 for 1 and 21 iterations respectively). Significance tests were performed with a Friedman 324 χ 2 with post hoc Bonferroni-corrected Wilcoxon signed-rank tests (significant at p < 0.017). n = 325 12 cells from 12 slices from 4 mice. Friedman χ 2 = 24, p = 6 × 10 −6 .

326
Finally we compared how deconvolution and refocusing affected lateral signal localization 327 compared to the equivalent wide field time series (Fig. 4h). We measured the width of radially av-328 eraged autocorrelations normalised to matched wide field trials for the refocused and deconvolved 329 cases. We found that the lateral signal spread significantly decreased from 1 to 21 iterations (me- rank tests on the raw widths (significant at p < 0.0083). n = 12 cells from 12 slices from 4 mice. 337 Friedman χ 2 = 26, p = 9 × 10 −6 .

338
In total our analyses reveal that deconvolution improves both axial and lateral signal local-339 ization, but decreases temporal signal SNR compared to synthetic refocussing, with both effects 340 intensifying with increasing iteration number. Points correspond to mean SNR between paired light field and wide field trials. Light field microscopy SNR does not differ significantly from wide field. For 8/12 trials we included a correction factor due to a misalignment in the LFM as discussed in section 2.3.3.

342
We measured the SNR for paired wide field and refocused light field imaging trials in the same 343 cells. For 8/12 trials we included a correction factor due to a misalignment in the LFM as discussed 344 in section 2.3.3. The SNR did not change significantly between the light field and wide field cases 345 (Wilcoxon signed rank test, n = 12 cells from 12 slices and 4 mice, z = 32, p = 0.6), with a median 346 light field SNR of 8.4 (5.2, 11.4) and a median wide field SNR of 10.0 (7.6, 11.9). 347 4 Discussion 348 We have shown that LFM enables 3D sub-cellular GEVI imaging of somatic and dendritic struc-349 tures. We demonstrated that LFM enables simultaneous imaging of axially separated dendrites, 350 overcoming a key limitation of wide field imaging. We further showed that functional voltage 351 signals from dendrites could be axially resolved at different depths. This finding is key to demon-352 strating LFM's utility for studies of dendritic integration or synaptic mapping. 353 We compared how synthetic refocussing and deconvolution-based reconstruction techniques 354 perform with respect to spatial signal localization and temporal SNR. Synthetic refocussing is 355 computationally simple and can be used to process light fields online, during an experiment, or 356 post hoc. Refocusing features better temporal signal SNR but poorer lateral and axial confinement 357 compared to deconvolution. Deconvolution has two major disadvantages: computational cost and In this study we imaged VSFP-Butterfly 1.2, an older generation probe. GEVI technology 371 has advanced dramatically recently, greatly increasing their sensitivity, and with these new sensors 372 noise amplification due to deconvolution in the light field volume reconstruction may become less 373 significant. Although VSFP-Butterfly 1.2 exhibits lower sensitivity than several recently reported 374 probes, 20, 79-83 we were able to express it sparsely and strongly to enable single-cell GEVI imag-375 ing without somatic restriction, which would preclude study of sub-cellular signals. 65,66 The slow 376 kinetics of the probe used in this study also enabled resolution of action potentials at 100 frames/s 377 without severe aliasing. Although we could resolve single-sweep signals, signal averaging was re-378 quired to resolve smaller dendritic signals with adequate SNR. With a more recent GEVI, dendritic 379 processes could likely be resolved in single sweeps. 380 Newer voltage sensors can not immediately be combined with LFM, however, as they require 381 much faster sampling rates, typically between 500 -1000 Hz. Megapixel cameras with 1 kHz full-382 frame readout rates are therefore needed to fully exploit these newer voltage indicators. Current 383 sCMOS cameras such as the one used in this study can achieve these imaging rates by reducing the 384 FOV to a small central strip of the image sensor. This, however, is particularly detrimental to LFM 385 compared to wide field imaging as the LFM PSF spreads information about each point widely 386 across the image sensor for objects away from the focal plane. If only a small strip of the sensor 387 is imaged SNR will be greatly degraded as light is lost outside of this reduced FOV. We anticipate 388 that this issue will be steadily ameliorated as faster sCMOS sensor technology is developed. 389 A second issue arises with newer, faster GEVIs due to their requirement for much faster frame 390 rates. Deconvolving individual frames with these sensors would require a drastic increase in com-391 putational resources and is likely untenable. Approaches have been developed for calcium imag-392 ing light field time series which do not involve deconvolution of every frame. 61, 84 In their current 393 form, however, these are unsuitable for reconstruction of subcellular light field voltage imaging 394 time series as they leverage the temporal and spatial characteristics of neuronal calcium imaging 395 as reconstruction priors. These priors, such as somatic signal localisation or sparse temporal activ-396 ity, are not as applicable to subcellular voltage imaging signals, which are smaller, less temporally 397 sparse and arise from more morphologically intricate structures than neuronal somata. 398 Finally, in this study we compared the SNR between refocused LFM volumes and matched 399 wide field traces and found they did not differ significantly. This is expected, as apart from light 400 losses at the MLA, which are < 15% according to the manufacturer, there are no significant losses 401 of SNR to shot noise between wide field and light field microscopy. Together these results have the 402 potential to motivate further work and widespread application of light field microscopy to voltage 403 imaging owing to light fields high photon budget and ability to resolve neurons in three spatial 404 dimensions. 405 Disclosures 406 The authors declare that the research was conducted in the absence of any commercial or financial 407 relationships that could be construed as a potential conflict of interest. 408 by remote-focusing and holographic light patterning," Proceedings of the National Academy